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A finite element approach for modeling photon transport in tissue
Author(s) -
Arridge S. R.,
Schweiger M.,
Hiraoka M.,
Delpy D. T.
Publication year - 1993
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.597069
Subject(s) - monte carlo method , physics , photon transport in biological tissue , photon , photon diffusion , monte carlo method for photon transport , finite element method , boundary value problem , mathematical analysis , computational physics , radiation flux , radiative transfer , diffusion equation , statistical physics , optics , mathematics , radiation , monte carlo molecular modeling , quantum mechanics , markov chain monte carlo , metric (unit) , light source , statistics , economics , thermodynamics , operations management
The use of optical radiation in medical physics is important in several fields for both treatment and diagnosis. In all cases an analytic and computable model of the propagation of radiation in tissue is essential for a meaningful interpretation of the procedures. A finite element method (FEM) for deriving photon density inside an object, and photon flux at its boundary, assuming that the photon transport model is the diffusion approximation to the radiative transfer equation, is introduced herein. Results from the model for a particular case are given: the calculation of the boundary flux as a function of time resulting from a δ‐function input to a two‐dimensional circle (equivalent to a line source in an infinite cylinder) with homogeneous scattering and absorption properties. This models the temporal point spread function of interest in near infrared spectroscopy and imaging. The convergence of the FEM results are demonstrated, as the resolution of the mesh is increased, to the analytical expression for the Green's function for this system. The diffusion approximation is very commonly adopted as appropriate for cases which are scattering dominated, i.e., where μ s ≫μ a , and results from other workers have compared it to alternative models. In this article a high degree of agreement with a Monte Carlo method is demonstrated. The principle advantage of the FE method is its speed. It is in all ways as flexible as Monte Carlo methods and in addition can produce photon density everywhere, as well as flux on the boundary. One disadvantage is that there is no means of deriving individual photon histories.